Advances in Difference Equations 
Volume 2005 (2005), Issue 3, Pages 345-367
doi:10.1155/ADE.2005.345

On the oscillation of certain third-order difference equations

Ravi P. Agarwal,1 Said R. Grace,2 and Donal O'Regan3

 1Department of Mathematical Sciences, Florida Institute of Technology, Melbourne 32901-6975, FL, USA
2Department of Engineering Mathematics, Faculty of Engineering, Cairo University, Orman, Giza 12221, Egypt
3Department of Mathematics, National University of Ireland, Galway, University Road, Galway, Ireland
Received 28 August 2004

Abstract

We establish some new criteria for the oscillation of third-order difference equations of the form Δ((1/a2(n))(Δ(1/a1(n))(Δx(n))α1)α2)+δq(n)f(x[g(n)])=0, where Δ is the forward difference operator defined by Δx(n)=x(n+1)−x(n).